Its easy...
PickAxe-The Instructor will give you one.
When? After you Prospect (Press RightMouseButton) and click Prospect. Prospect both colors, then talk to the Instructor.
You dont need to click the PickAxe, just click both colors untill you get a new item. Talk again.
You will be asked to smelt them. Just press one, then click the Furnace (Big black thing).
You will get a Brown bar (Bronze bar).
You will have a Hammer too, click the bar, then click the anvil (Small silver thing).
It is right beside the Furnace.
Congradulations! You have completed the Mining and Smelting tutoral.